The derivation of thermo-physical properties and phase equilibria of silicate materials from lattice vibrations: Application to convection in the Earth’s mantle

Jacobs, M.H.G.; Berg, A. P. van den; Jong, B.H.W.S. de

doi:10.1016/j.calphad.2005.10.001

Cited by 24 publications

(30 citation statements)

References 73 publications

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“…Nevertheless, it has been shown that HT-BM3-EOS is prone to giving spurious effects or anomalous predictions (i.e., negative thermal expansion) at very HP-HT conditions [63,113]. This has led different authors to develop alternative formulations (more or less empirical) to describe the P-V-T relations of minerals up to planetary interior conditions [4,63,78,[113][114][115][116][117][118][119]. Even though negative thermal expansion is obviously possible from a physical point of view as different minerals and compounds display a volume decrease with T not just in the low-P range [25,120], this phenomenon is systematically predicted by the HT-BM3-EOS at very HP-HT conditions.…”

Section: Phase Equilibrium Calculation At Hp-ht: Modelling High-pressmentioning

confidence: 99%

First Principles Thermodynamics of Minerals at HP–HT Conditions: MgO as a Prototypical Material

Belmonte

2017

Minerals

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Ab initio thermodynamic properties, equation of state and phase stability of periclase (MgO, B1-type structure) have been investigated in a broad P-T range (0-160 GPa; 0-3000 K) in order to set a model reference system for phase equilibria simulations under deep Earth conditions. Phonon dispersion calculations performed on large supercells using the finite displacement method and in the framework of quasi-harmonic approximation highlight the performance of the Becke three-parameter Lee-Yang-Parr (B3LYP) hybrid density functional in predicting accurate thermodynamic functions (heat capacity, entropy, thermal expansivity, isothermal bulk modulus) and phase reaction boundaries at high pressure and temperature. A first principles Mie-Grüneisen equation of state based on lattice vibrations directly provides a physically-consistent description of thermal pressure and P-V-T relations without any need to rely on empirical parameters or other phenomenological formalisms that could give spurious anomalies or uncontrolled extrapolations at HP-HT. The post-spinel phase transformation, Mg 2 SiO 4 (ringwoodite) = MgO (periclase) + MgSiO 3 (bridgmanite), is taken as a computational example to illustrate how first principles theory combined with the use of hybrid functionals is able to provide sound results on the Clapeyron slope, density change and P-T location of equilibrium mineral reactions relevant to mantle dynamics.

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Section: Phase Equilibrium Calculation At Hp-ht: Modelling High-pressmentioning

confidence: 99%

First Principles Thermodynamics of Minerals at HP–HT Conditions: MgO as a Prototypical Material

Belmonte

2017

Minerals

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“…[20] proposed a method to mimic the phonon frequencies by a series of Einstein oscillator with certain frequency. Greeff et al [29] performed electronic structure calculations of frozen phonon frequencies for Cu and interpolated to obtain the phonon frequencies throughout the Brillouin zone from which they can take average to evaluate effective Debye temperatures.…”

Section: Helmholtz Energy Of Electron Gas F El (Tv)mentioning

confidence: 99%

“…While the CALPHAD technique uses Gibbs energy for the sake of convenience to practical constant temperature and pressure applications, theoretical work adopts naturally Helmholtz energy because ab initio calculations are always performed at constant temperature and volume [see for example, [16][17][18][19][20]. When the temperature and volume dependence of Helmholtz energy is established with some physical models, other thermodynamic properties including thermophysical properties can be derived in an intrinsically consistent way, and thus abnormal behaviors can be avoided for properties at high temperatures and high pressures.…”

Section: Introductionmentioning

confidence: 99%

A CALPHAD Helmholtz energy approach to calculate thermodynamic and thermophysical properties of fcc Cu

Lu¹,

Chen²

2009

Philosophical Magazine

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“…From the Helmholtz energy we derived the equation of state, partitioned in a static lattice and a vibrational part as is summarized in Appendix 1 for pure endmembers. That results in the volume of the static lattice, which enables the comparison of our results with static ab initio results as was done for perovskite in Jacobs et al (2006). Rewriting Eq.…”

Section: Theoretical Backgroundmentioning

confidence: 84%

“…Because our vibrational model incorporates more physical properties relative to polynomial models used by, e.g., Fabrichnaya (1998), Holland and Powell (1998), Saxena (1996) and used in our previous work Jacobs and de Jong (2005b), the thermodynamic description of substances is more unambiguously constrained. For instance, in Jacobs et al (2006) we have shown for c-Mg 2 SiO 4 that this results in a better discrimination of the quality of different experimental data sets. Another example is MgSiO 3 perovskite for which a description based on lattice vibrations results in a more reliable extrapolation of thermodynamic properties to regions in pressure-temperature space, which are difficult to access experimentally.…”

Section: Introductionmentioning

confidence: 93%

Thermodynamic mixing properties of olivine derived from lattice vibrations

Jong

2009

Phys Chem Minerals

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We use a lattice vibrational technique to derive thermophysical and thermochemical properties of fayalite, Fe 2 SiO 4 . This semi-empirical technique is based on an extension of Kieffer's model to incorporate details of the phonon spectrum. It includes treatment of intrinsic anharmonicity and electronic effects based on crystal field theory. We extend it to predict thermodynamic mixing properties of olivine (Mg,Fe) 2 SiO 4 solid solutions by using results of our previous work on the system MgO-SiO 2 . Achieving this requires a relation between phonon frequency and composition and a composition relation for the energy of the static lattice. Directed by experimental Raman spectroscopic data for specific optic modes in magnesium-iron solid solutions of olivine and pyroxene we use an empirical relation for the composition dependence for phonon frequencies. We show that lattice vibrations have a large effect on the excess entropy and that the static lattice contribution and lattice vibrations have a large impact on excess enthalpy and excess Gibbs energy. Our model indicates that compositional effects in electronic and magnetic properties are negligible. The compositional variation the Néel temperature has a large impact on excess heat capacity for temperatures below 100 K.

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The derivation of thermo-physical properties and phase equilibria of silicate materials from lattice vibrations: Application to convection in the Earth’s mantle

Cited by 24 publications

References 73 publications

First Principles Thermodynamics of Minerals at HP–HT Conditions: MgO as a Prototypical Material

First Principles Thermodynamics of Minerals at HP–HT Conditions: MgO as a Prototypical Material

A CALPHAD Helmholtz energy approach to calculate thermodynamic and thermophysical properties of fcc Cu

Thermodynamic mixing properties of olivine derived from lattice vibrations

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